Large Language Models (LLMs) represent a new frontier of digital infrastructure that can support a wide range of public-sector applications, from general purpose citizen services to specialized and sensitive state functions. When expanding AI access, governments face a set of strategic choices over whether to buy existing services, build domestic capabilities, or adopt hybrid approaches across different domains and use cases. These are critical decisions especially when leading model providers are often foreign corporations, and LLM outputs are increasingly treated as trusted inputs to public decision-making and public discourse. In practice, these decisions are not intended to mandate a single approach across all domains; instead, national AI strategies are typically pluralistic, with sovereign, commercial and open-source models coexisting to serve different purposes. Governments may rely on commercial models for non-sensitive or commodity tasks, while pursuing greater control for critical, high-risk or strategically important applications. This paper provides a strategic framework for making this decision by evaluating these options across dimensions including sovereignty, safety, cost, resource capability, cultural fit, and sustainability. Importantly, "building" does not imply that governments must act alone: domestic capabilities may be developed through public research institutions, universities, state-owned enterprises, joint ventures, or broader national ecosystems. By detailing the technical requirements and practical challenges of each pathway, this work aims to serve as a reference for policy-makers to determine whether a buy or build approach best aligns with their specific national needs and societal goals.